1. Field of the Invention
The present invention relates to an image processing method, an image processing apparatus, and a computer-readable recording medium that records an image processing program for processing a stained-sample image obtained by imaging a sample which is stained with a predetermined staining dye.
2. Description of the Related Art
For example, in pathological diagnosis, a method is widely used such that a tissue specimen obtained by removal of an organ or needle biopsy is thinly sliced to obtain a sample having a thickness of a few microns, and magnification observation is made with a microscope in order to acquire various findings. Particularly, transmission observation using an optical microscope is one of the most popular observation methods for reasons such that devices are relatively inexpensive and easy to handle, and the method has long history. In this case, a specimen removed from a living body hardly absorbs and scatters light and is nearly clear and colorless. Consequently, at the time of creation of a sample, the specimen is generally stained with a dye.
Various staining methods are proposed and the total number thereof rises to 100 or larger. Particularly, for a pathological sample, hematoxylin-eosin staining (hereinbelow, called “H&E staining”) is normally employed. The H&E staining uses blue-purple hematoxylin (referred to as “dye H” below) and red eosin (referred to as “dye E” below) as staining dyes. In a sample subjected to the H&E staining (stained sample), a cell nucleus, a bone tissue, and the like are stained in blue-purple, and a cytoplasm, a connective tissue, a red blood cell, and the like are stained in red, so that they can be easily visually recognized. As a result, an observer can grasp sizes, positional relations, and the like of components of the tissue such as the cell nucleus and morphologically determine a state of the sample.
A stained sample is observed visually or a stained sample which is imaged and displayed on a display device is observed. An attempt to process and analyze a stained-sample image and support observation and diagnosis of a doctor and the like is proposed. As an example, there is a conventionally known method of quantitatively estimating the amount of a staining dye with which a point on a stained sample (sample point) is stained on the basis of a stained-sample image obtained by performing multiband imaging on the stained sample, and the method is applied to various purposes. For example, a method for estimating a dye amount and correcting color information of a stained-sample image on the basis of the estimated dye amount is disclosed in “Color Correction of Pathological Images Based on Dye Amount Quantification”, OPTICAL REVIEW Vol. 12, No. 4 (2005), pp. 293-300. A method of quantitatively evaluating a stained state of a sample on the basis of an estimated dye amount is disclosed in “Development of Support Systems for Pathology using Spectral Transmittance—The quantification Method of Stain Conditions”, Proceedings of SPIE, Image Processing, Vol. 4684 (2002), pp. 1516-1523. Japanese Laid-open Patent Publication No. 2005-331394 discloses a method of classifying tissues in a sample on the basis of an estimated dye amount and dividing an image into regions on a tissue unit basis.
A method of quantitatively estimating a dye amount from a stained-sample image (multiband image) will be described using a sample subjected to the H&E staining as an example. Prior to estimation of a dye amount, for example, the background without a sample is imaged in a state where illumination light is irradiated to capture a multiband image of the background (illumination light). First, the multiband image of the background is set as I0, a multiband image of a stained sample to be observed is set as I, and spectral transmittance t(x,λ) in each pixel position is calculated by the following Equation (1). Here, x denotes a position vector expressing a pixel in the multiband image, and λ denotes wavelength. I(x,λ) expresses a pixel value in a pixel position (x) at the wavelength λ of a multiband image I, and I0(x,λ) expresses a pixel value in a pixel position (x) at the wavelength λ of the multiband image I0.
                              t          ⁡                      (                          x              ,              λ                        )                          =                              I            ⁡                          (                              x                ,                λ                            )                                                          I              0                        ⁡                          (                              x                ,                λ                            )                                                          (        1        )            
Regarding the spectral transmittance t(x,λ), the Lambert-Beer law is satisfied. For example, in the case where a sample is stained with two staining dyes of the dyes H and E, the following Equation (2) is satisfied at each wavelength λ by the Lambert-Beer low.−log t(x,λ)=kH(λ)dH(x)+kE(λ)dE(x)  (2)
In Equation (2), kH(λ) and kE(λ) are coefficients unique to a substance and determined depending on the wavelength λ. For example, kH(λ) indicates a coefficient corresponding to the dye H, and kE(λ) represents a coefficient corresponding to the dye E. For example, the values of kH(λ) and kE(λ) are dye spectral characteristic values of the dyes H and E with which a sample is stained (hereinbelow, the dye spectral characteristic value of a dye with which a sample is stained will be called “reference spectrum”). dH(x) and dE(x) correspond to amounts of the dyes H and E at each of the sample points in the stained sample corresponding to the pixel positions (x) in a multiband image. More specifically, when the amount of the dye H in a sample stained only with the dye H is set as “1”, dH(x) is obtained as a value relative to the dye amount. Similarly, when the amount of the dye E in a sample stained only with the dye E is “1”, dE(x) is obtained as a value relative to the dye amount. The dye amount is also called density.
Equation (2) is satisfied independently every wavelength λ. Equation (2) is a linear equation of dH(x), dE(x), and a method of solving it is generally known as multiple linear regression analysis. For example, by using simultaneous Equations (2) for two or more different wavelengths, they can be solved.
For example, when the equations are simultaneously used for M (M≧2) wavelengths λ1, λ2, . . . , μM, they can be expressed as the following Equation (3). [ ]t shows a transposed matrix, and [ ]−t expresses an inverse matrix.
                              [                                                                                          -                    log                                    ⁢                                                                          ⁢                                      t                    ⁡                                          (                                              x                        ,                                                  λ                          1                                                                    )                                                                                                                                                                -                    log                                    ⁢                                                                          ⁢                                      t                    ⁡                                          (                                              x                        ,                                                  λ                          2                                                                    )                                                                                                                          ⋮                                                                                      log                  ⁢                                                                          ⁢                                      t                    ⁡                                          (                                              x                        ,                                                  λ                          M                                                                    )                                                                                                    ]                =                              [                                                                                                      k                      H                                        ⁡                                          (                                              λ                        1                                            )                                                                                                                                  k                      E                                        ⁡                                          (                                              λ                        1                                            )                                                                                                                                                              k                      H                                        ⁡                                          (                                              λ                        2                                            )                                                                                                                                  k                      E                                        ⁡                                          (                                              λ                        2                                            )                                                                                                                    ⋮                                                  ⋮                                                                                                                        k                      H                                        ⁡                                          (                                              λ                        M                                            )                                                                                                                                  k                      E                                        ⁡                                          (                                              λ                        M                                            )                                                                                            ]                    ⁡                      [                                                                                                      d                      H                                        ⁡                                          (                      x                      )                                                                                                                                                              d                      E                                        ⁡                                          (                      x                      )                                                                                            ]                                              (        3        )            
When Equation (3) is solved by using least-squares estimation, the following Equation (4) is obtained. An estimation value {circumflex over (d)}H(x) of the amount of the dye H and an estimation value {circumflex over (d)}E(x) of the amount of the dye E are obtained.
                              [                                                                                                                d                      ^                                        H                                    ⁡                                      (                    x                    )                                                                                                                                                                  d                      ^                                        E                                    ⁡                                      (                    x                    )                                                                                ]                =                                                                              (                                                                                    [                                                                                                                                                                              k                                  H                                                                ⁡                                                                  (                                                                      λ                                    1                                                                    )                                                                                                                                                                                                                      k                                  E                                                                ⁡                                                                  (                                                                      λ                                    1                                                                    )                                                                                                                                                                                                                                                                          k                                  H                                                                ⁡                                                                  (                                                                      λ                                    2                                                                    )                                                                                                                                                                                                                      k                                  E                                                                ⁡                                                                  (                                                                      λ                                    2                                                                    )                                                                                                                                                                                                        ⋮                                                                                      ⋮                                                                                                                                                                                                            k                                  H                                                                ⁡                                                                  (                                                                      λ                                    M                                                                    )                                                                                                                                                                                                                      k                                  E                                                                ⁡                                                                  (                                                                      λ                                    M                                                                    )                                                                                                                                                                    ]                                            t                                        ⁡                                          [                                                                                                                                                                  k                                H                                                            ⁡                                                              (                                                                  λ                                  1                                                                )                                                                                                                                                                                                        k                                E                                                            ⁡                                                              (                                                                  λ                                  1                                                                )                                                                                                                                                                                                                                                        k                                H                                                            ⁡                                                              (                                                                  λ                                  2                                                                )                                                                                                                                                                                                        k                                E                                                            ⁡                                                              (                                                                  λ                                  2                                                                )                                                                                                                                                                                          ⋮                                                                                ⋮                                                                                                                                                                                              k                                H                                                            ⁡                                                              (                                                                  λ                                  M                                                                )                                                                                                                                                                                                        k                                E                                                            ⁡                                                              (                                                                  λ                                  M                                                                )                                                                                                                                                        ]                                                        )                                                  -                  1                                            ⁡                              [                                                                                                                              k                          H                                                ⁡                                                  (                                                      λ                            1                                                    )                                                                                                                                                              k                          E                                                ⁡                                                  (                                                      λ                            1                                                    )                                                                                                                                                                                                  k                          H                                                ⁡                                                  (                                                      λ                            2                                                    )                                                                                                                                                              k                          E                                                ⁡                                                  (                                                      λ                            2                                                    )                                                                                                                                                ⋮                                                              ⋮                                                                                                                                                    k                          H                                                ⁡                                                  (                                                      λ                            M                                                    )                                                                                                                                                              k                          E                                                ⁡                                                  (                                                      λ                            M                                                    )                                                                                                                    ]                                      t                    ⁢                                          ⁢                                          [                                          ⁢                                                                                          -                    log                                    ⁢                                                                          ⁢                                      t                    ⁡                                          (                                              x                        ,                                                  λ                          1                                                                    )                                                                                                                                                                -                    log                                    ⁢                                                                          ⁢                                      t                    ⁡                                          (                                              x                        ,                                                  λ                          2                                                                    )                                                                                                                          ⋮                                                                                      log                  ⁢                                                                          ⁢                                      t                    ⁡                                          (                                              x                        ,                                                  λ                          M                                                                    )                                                                                                    ]                                    (        4        )            
By Equation (4), the estimation values of the amounts of the dyes H and E in an arbitrary sample point on a stained sample are obtained.